Bungee
MTS Data Collection
A variety of rubber band configurations were tested on an MTS machine, measuring force vs. displacement rather than the standard stress vs. strain data since the cross sectional area changes as the rubber is stretched. This data was compiled along with the full class dataset to have a 95% confidence interval accounting for variations in rubber bands. A cubic function was fit to the data due to the hyper elastic properties of rubber. We used this in our MatLab model, using energy calculations to determine the dynamic properties of different bungee configurations.
MatLab Model
Our model consists of an input and graphing script and 3 functions. The given information for this project was a range of input variables: object mass between 0.2-2 kg, a G-limit on acceleration between 4-7 G’s, and a range of drop heights between 6-100 ft. Given a set of inputs the first function iterates through a range of configuration parameters for the length of string, number of bands in series, and number of bands in parallel. This function checks whether each configuration doesn’t hit the ground or exceed the G-limit. The other two functions calculate the transfer from potential to spring energy, using the spring force function fit from our data, to determine the maximum extension of the bands. I made a MatLab script to plot the solutions on a 3D figure so we could visualize the range of possible configurations and the free fall “score” associated with each. This proved extremely useful for our model debugging and validation testing to build an intuition for which solutions made sense and also see the sensitivities to different parameters.
Validating the Model
We used our MatLab model to calculate configurations for smaller test drops and assembled a bungee with a weight and accelerometer attached to test the predicted performance. The accelerometer data helped us eliminate errors and verify that the model was working correctly at the small scale, giving us confidence that it would work at the large scale.
When all the accelerometers were inevitable broken by the class testing unreliable bungee’s, I repurposed a MatLab script I wrote for a previous class that was originally used to calculate G’s using video point tracking for a car crash test. We tested the final versions of our model by taking slow motion video at 240 frames per second, and using this script to track the motion, resulting in the graph on the left. The results were actually quite accurate, giving a maximum acceleration of ~6 G’s for a 7 G limit. We also confirmed the accuracy of this method by using it on the final drop video and comparing with the onboard accelerometer.
Final Drop
We were given the drop conditions 30 minutes before our drop time, then determined our configuration and assembled it. Given a drop height of 13.5 meters (4 stories), a mass of 0.993 kg, and a G-limit of 7 G’s, we used our validated model to calculate an ideal configuration to maximize free fall without hitting the ground or exceeding the G-limit. Our configuration came out to be 8.2 meters of string followed by 9 parallel sets of 39 folded rubber bands in series, resulting in a free fall of 9.76 meters. Since we ran into a few issues in testing where the string would become tangled, I researched a quick deploy winding for the string (seen in the top image) where it keeps the strings neatly coiled in storage and when released unravels without getting tangled.
Using the more conservative functions within the 95% confidence interval as a safety factor, this configuration was predicted to come just under the limitations. This is necessary since our model optimized to be mathematically less than or equal to the limits, meaning the initial prediction was very close to the limits. The safety factor also accounts for variations and imperfections in the rubber bands and the manufacturing methods. In our final drop, the GI-Joe test subject came within 10 centimeters of the ground, reaching a peak acceleration of 5.8 G’s, with a free fall time of 1.5 seconds. The video was taken at 240 frames per second, showing the bottom of the drop zone.
Project Summary
Bungee is a lab project for my Junior year MEAM Lab class. I worked in a group of 3 given loose guidelines to come up with a solution for a rubber band bungee jump.
The guidelines were intentionally broad, giving a range of input variables: object mass between 0.2-2 kg, a G-limit on acceleration between 4-7 G’s, and a range of drop heights between 6-100 ft. We were tasked with coming up with a model that takes in these variables and outputs the ideal bungee configuration to maximize the free fall time, with only 30 minutes before the final test to run the model and assemble our bungee.
We started by characterizing the force vs. displacement properties of the rubber bands and used this data in a MatLab model to determine the dynamics given different input variables. The model varies the input parameters to optimize for free fall distance while staying within the constrains to tell us what configuration of bungee is best. I wrote an output visualization for the model which helped us understand what was happening as we changed things with the model and varied inputs. We conducted several small scale tests to debug and calibrate our model until we were confident its predictions were reasonably accurate. I modified an old script I wrote for a different class which uses point tracking to plot position, velocity, and acceleration graphs from video to help verify the model. Noticing issues with the string getting tangled during test drops, I looked up ways to fold the string such that it could unwind quickly and tangle-free, something not many other teams though to do leading to problems while collecting data and even at the final test.
The full scale performance of our model was about as good as we could hope for. From a drop of 13.5 meters (4 stories) the mass came within 10 centimeters of the ground with a free fall time of 1.5 seconds while reaching 5.8 G’s of the 7 G Limit, one of the best in the class.
Team Members: Lucy Stinn, Noah Kamerling